From: Lee Corbin (lcorbin@tsoft.com)
Date: Fri Jun 07 2002 - 16:22:51 MDT
Spike writes
> Start with the sequence 3*5. To make a better number, what
> is the third term ideally?
>
> 3*5*n = (3+1)*(5+1)*(n+1) - 3*5*n
>
> n = 4, even, so 3*5*4 is even so no odd perfect number
> for the good guys.
>
> Repeat for 3*5*7*11*n, we get n=384, even. Im thinking
> now there is a trivial proof why it should always be so.
Yes, because from
> 3*5*n = (3+1)*(5+1)*(n+1) - 3*5*n
we have
> 3*5*n + 3*5*n = (3+1)*(5+1)*(n+1)
and the question is (I infer) why is n always even?
Well, the right hand side is WAY even, since all
its factors except the last (maybe) are. So
dividing both sides by 2, we get
3*5*n = [ (3+1)/2 ] * (5+1) * (n+1)
and so n must be even because (5+1) is.
Lee
P.S. Thanks for the kind proposal to name the formula
for finding the sum of divisors after me, but Euclid
beat me out by about 2300 years. :-)
> >This is a model for the way that we want to explode
> >into the future... Lee
> >
> Wow, cool thought Lee. I was about to suggest we start
> ExI-math to avoid distubing those who are offended by
> mathematics. {8^D
My only regret is that I didn't name the thread
"Spiking into the future". I *knew* there had
to be a connection between Damien Broderick's
book about the Singularity ("The Spike"), and
your name, but I never groked it till now :-D
> Shall we start ExI-math and take this elsewhere? Or trust
> non-math-geeks to be quick on the delete key? spike
I dunno.
Lee
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